the wee hours (of the night/morning)
The very early hours after midnight. I was studying for the exam until the wee hours of the morning, and now I can barely keep my eyes open! We all danced until the wee hours of the night. I love the wee hours, when few are awake and one can be alone with one's thoughts.
wee hours
The early hours of the morning right after midnight: "post-disco electronic rhythms that propel clubgoers into the wee hours" (Jon Pareles).